Population Growth and Regulation: Life Tables - Ecology | IB 203, Study notes of Ecology and Environment

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Chapter 9A (Population Growth and Regulation: Life Tables) Major Concepts 1. Life tables show how survival and reproductive rates vary with age, size, or life- cycle stage. 2. Life table data can be used to project the future age structure, size, and growth rate of a population. Objectives 1. Explain the structure of a life table, which data are field collected vs. derived, and the various formulae involved. 2. Compare cohort vs. static life tables and explain when each are used and their limitations. 3. Calculate all values for a life table based on field data. 4. Demonstrate understanding of log scales by graphing survivorship data. 5. Interpret whether death rate is constant and conclude the type of survivorship curve 6. Calculate life expectancy and interpret what a value means. 7. Using data from a life table, calculate population growth parameters and interpret whether a population is growing, stable, or declining. 8. Explain what generation time means. 9. Compare age structures and predict potential for future population growth. 10. Use life table data to project future age structure, size, and growth rate of a population. 11. Analyze whether a population has reached a stable age distribution. Summary Concept 9.1 Life tables show how survival and reproductive rates vary with age, size, or life cycle stage.  Cohort life tables can be constructed from data on the fates of individuals born during the same time period and used to calculate age-specific survival rate, survivorship, and fecundity.  In highly mobile or long-lived organisms, a static life table may be constructed from data on the survival and fecundity of individuals of different ages during a single time period.  In species for which age correlates poorly with survival and fecundity, life tables based on size or life cycle stage may be constructed.  In populations with a type I survivorship curve, most individuals survive to old age. In populations with a type II survivorship curve, individuals experience a constant chance of surviving from one age to the next throughout their lives. In populations with a type III survivorship curve, death rates are very high for young individuals, but adults survive well later in life. Of the three types, type III is the most common. Concept 9.2 Life table data can be used to project the future age structure, size, and growth rate of a population.  The age structure of a population influences the growth rate of that population over time.  A population eventually grows at a fixed rate if age-specific survival rates and fecundities do not change over time.  Any factor that changes age-specific survival rates or fecundities may alter a population’s growth rate.
Vocab  Life table: summary of how survival and reproductive rates in a population vary with the age of individuals; in species for which age is not informative or is difficult to measure, life tables may be based on the size or life history stage of individuals.  Survival rate (Sx): Proportion of individuals of age x that survive to be age x + 1.  Survivorship (lx): Proportion of individuals that survive from birth (age 0) to age x.  Fecundity Fx (or mx): Average # of offspring produced by a female while she is age of x.  Life expectancy ex: Expected number of years of life remaining.  Cohort life table: A life table in which the fate of a group of individuals born during the same time period (a cohort) is followed from birth to death.  Static life table: A life table that records the survival and reproduction of individuals of different ages during a single time period.  Survivorship curve (I, II or III): A graph based on survivorship data (lx) that plots the number of individuals from a hypothetical cohort (typically, of 1,000 individuals) that will survive to reach different ages.  Age Class: member of a population whose ages fall within a specified range.  Age Structure: proportions of a population in each age class  Population growth Rate ( = Nt+1/ Nt): a change in abundance over one time step. Concept 9.5 The logistic equation incorporates limits to growth and shows how a population may stabilize at a maximum size, the carrying capacity.  In some species, changes in population size over time can be described by an S- shaped curve in which the population increases rapidly at first, then stabilizes at a maximum level, the carrying capacity.  The logistic equation can be used to represent density-dependent population growth.  Logistic population growth provides a close fit to the size of the U.S. population up to 1950; after that time, the growth rate of the U.S. population was considerably greater than expected in logistic growth.  Over the past 2,000 years, the human population has increased in size even more rapidly than it would if it were growing exponentially.  Estimates of the carrying capacity of the human population vary widely, from fewer than 1 billion people to more than 1,000 billion people.  The carrying capacity concept applies poorly to human populations that import resources from outside the area in which the population is found.  Ecological footprint analyses based on available productive land area and current patterns of resource use suggest that the global human population is 40% greater than the maximum number that could be sustained for a long time. Vocab  Geometric growth (J-shape) : λ (aka finite rate of increase) 1. Nt+1 =  Nt 2. Nt+1 = t N0 3. Discrete time period  Geometric pop. Growth rate = finite rate of growth  Exponential pop. Growth rate = r = (per capita) intrinsic rate of increase: shows how rapidly a population can grow * Both geometric growth and exponential growth results the same shaped graph (J-shaped). However, geometric growth results in J-shaped set of points (dots) whereas exponential growth has in a J-shaped curve (line). *  Doubling Time (td = ln ⁡(2) r ): # of years that will take the population to double in size  Net reproductive rate R0⁡= Σ lx Fx:⁡mean number of offspring produced by individual through lifetime.  Exponential growth (J-shape): when a population of a species with continuous reproduction changes in size by a constant proportion at each instant in time. 1. dN dt = rN 2. Nt=N0ert (e=2.718)  Density-dependent factor: cause birth/death rates and dispersal rates to change as the density of population changes.  Density-independent factor: factors’ effects on birth and death rates are independent of number of individuals in the population. (ex: temperature, precipitation, and floods)  Population regulation: when one or more density-dependent factors cause population size to increase when numbers are low and decrease when numbers are high.  Logistic growth (S-shape): a pattern in which its abundance increases rapidly at first, then stabilizes at a population size (Carrying capacity) 1. dN dt =rN (1− N K ) 2. dN dt =rN (K− N K )  Carrying capacity (K): maximum population size that can be supported indefinitely by the environment. (@ carrying capacity, growth rate = zero; therefore, no pop. size change) Chapter 10 Population Dynamics Major Concepts: 1.Populations exhibit a wide range of growth patterns, including exponential growth, logistic growth, fluctuations, and regular cycles. 2.Delayed density dependence can cause populations to fluctuate in size. 3.The risk of extinction increases greatly in small populations. 4.Many species have a metapopulation structure in which sets of spatially isolated populations are linked by dispersal. Objectives: 1. Associate population growth rates to birth and death rates; associate changes in birth and death rates to changes in population equilibrium and carrying capacity. 2. Analyze a figure and describe results. Interpret the results in terms of delayed density dependence affecting population fluctuations. 3. Compare results from sequence of experiments and relate how they test the hypothesis of delayed density dependence. 4. In a metapopulation, predict what factors are barriers to movement in a matrix. 5. Analyze a figure and identify two variables affecting colonization probabilities. 6. Compare a source subpopulation to a sink population in terms of directionality of immigration flow. 7. Set up a model of metapopulation dynamics by hypothesizing factors affecting spatial pattern of subpopulation over time. Summary Concept 10.1 Populations exhibit a wide range of growth patterns, including exponential growth, logistic growth, fluctuations, and regular cycles.  Most observed patterns of population growth can be grouped into four major types. These four patterns are not mutually exclusive, and a single population can experience each of them at different times.  The first pattern, exponential growth, can occur for a limited time when conditions are favorable.  The second pattern, logistic growth, is found in populations that increase initially and then level off at a maximum population size, the carrying capacity.  The third pattern, population fluctuations, is found in all populations. Some populations fluctuate greatly over time; others fluctuate relatively little.  The fourth pattern, regular population cycles, is a special type of fluctuation in which alternating periods of high and low abundance occur after nearly constant intervals of time. Concept 10.2 Delayed density dependence can cause populations to fluctuate in size.  There is often a time lag between a change in population density and the effect that change has on future population densities.